Hedge-fund manager Bill Ackman spelled out his bullish case on housing firms Fannie Mae and Freddie Mac, calling them “essential” to the U.S. mortgage market.

Fannie Mae and Freddie Mac, who both trade over the counter at around $4, are worth $23 on a conservative basis, he said, and could be worth as much as $47. The comments by Mr. Ackman of Pershing Square Capital Management marked the first time he specifically laid out his optimistic thesis for Fannie and Freddie. He spoke at the Sohn Investment Conference in New York.

Pershing Square owns about 10% of the firms’ common shares. In filings last November, Pershing Square said it had spent about $400 million on its investments.

Mr. Ackman called for Fannie and Freddie to build much stronger capital ratios to protect against large defaults. They should also get out of insuring subprime mortgages and so-called Alt-A mortgages that caused much of the trouble during the financial crisis. The 30-year fixed-rate mortgage, he said, should remain the basic building block for the housing market.

Fannie and Freddie have “enabled a very strong housing market apart from the bubble and the bubble bursting,” Mr. Ackman said. They are “essential to preserving the housing market.”

Mr. Ackman has joined a growing who’s who of distressed-equity investors, including Bruce Berkowitz’s Fairholme Capital Management, Richard Perry’s Perry Capital, and John Paulson‘s Paulson & Co., in betting on the revival of Fannie and Freddie.

Mr. Ackman’s investment is a bet that Congress and the White House ultimately won’t follow through on pledges to liquidate Fannie and Freddie. Lawmakers, the thinking goes, will conclude that getting rid of the companies could do unnecessary damage to the mortgage market and that any desired market overhaul could be accomplished by restructuring rather than replacing the companies.

The new, private-label Fannie and Freddie that have been proposed by lawmakers would have to raise up to $500 billion to capitalize them, Mr. Ackman said. But the history of the government having “stolen” the dividends makes that unlikely.

Mr. Ackman was referring to changes that took effect last year requiring Fannie and Freddie to send all of their profits to the U.S. Treasury as dividends for their 2008 bailouts. Previously, the companies were required to pay a 10% annual dividend on the $187.5 billion that the government injected in both companies. Messrs. Berkowitz and Perry are among the investors whose firms have sued the government, arguing that the “profit sweep” was unconstitutional.

Given the way investors have been treated by those changes, “we don’t think there’s an investor in the world of any consequence that will invest in the new version of Fannie and Freddie,” he says.

“We don’t think there’s an investor in the world of any consequence that will invest in the new version of Fannie and Freddie,” he says.

Mr. Ackman said there’s no comparison between other recent proposals to reform the mortgage market and what he’s come up with. A big reason his proposal is palatable, he said, is that taxpayers would see billions of dollars in windfall from Fannie and Freddie, he says, with profits going to infrastructure and other needs.